Category:Inductive Sets

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This category contains results about Inductive Sets.

Let $S$ be a set of sets.

Then $S$ is inductive if and only if:

\((1)\)   $:$   $S$ contains the empty set:    \(\displaystyle \quad \O \in S \)             
\((2)\)   $:$   $S$ is closed under the successor mapping:      \(\displaystyle \forall x:\) \(\displaystyle \paren {x \in S \implies x^+ \in S} \)             where $x^+$ is the successor of $x$
         That is, where $x^+ = x \cup \set x$